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本文提出一种基于零折射率介质的超窄带光学滤波器. 在线缺陷光学滤波器中引入具有类狄拉克点的光学超构材料, 利用其零折射效应来实现滤波带宽的压缩. 基于COMSOL Multiphysics软件的传输特性分析表明, 当超构材料的类狄拉克点频率与缺陷态的谐振频率相符合时, 光学滤波器的透射峰能够显著压缩; 光场分布及等效介质分析表明, 零折射率介质的零相位延迟效应与强色散特性能够增强缺陷态透射电磁响应随频率变化的灵敏度, 提高滤波器的品质因子, 并能在压缩滤波带宽的同时保持高的峰值透射率, 实现高耦合、超窄带的滤波设计. 该结果为基于光学超构材料的波分复用系统设计与应用提供了新的技术思路.Owing to the photonic band gap effect and defect state effect, photonic metamaterials have received much attention in the design of narrow bandpass filters, which are the key devices of optical communication equipment such as wavelength division multiplexing devices. In this work, based on zero-index metamaterial (ZIM), a compact filter with both high peak transmission coefficient and ultra-narrow bandwidth is proposed. The photonic metamaterial with conical dispersion and Dirac-like point is achieved by optimizing the structure and material component parameters of dielectric rods with square lattice in air. It is demonstrated that a triply degenerate state can be realized at the Dirac-like point, which relates this metamaterial to a zero-index medium with effective permittivity and permeability equal to zero simultaneously. Electromagnetic (EM) wave can propagate without any phase delay at this frequency, and strong dispersion occurs in the adjacent frequency cone, leading to dramatic changes in optical properties. We introduce a ZIM into photonic metamaterial defect filter to compress the bandwidth to the realization of ultra-narrow bandpass filter. The ZIM is embedded into the resonant cavity of line defect filter, which is also composed of dielectric rods with square lattice in air. In order to increase the sensitivity of the phase change with frequency, the Dirac-like frequency is adjusted to match the resonant frequency of the filter. We study the transmission spectrum of the structure through the COMSOL Multiphysics simulation software, and find that the peak width at half-maximum of the filter decreases as the thickness of ZIM increases, and the peak transmittance is still high when bandwidth is greatly compressed. The zero phase delay inside the slab can be observed. Through field distribution analysis, the zero-phase delay and strong coupling characteristics of electromagnetic field are observed at peak frequency. The comparison with conventional photonic metamaterials filter is discussed. We believe that this work is helpful in investigating the realization of ultra-narrow bandpass filters.
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Keywords:
- photonic metamaterials /
- narrow-band filter /
- zero-index /
- Dirac-like point
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图 1 滤波器结构示意图 (a)线缺陷滤波器; (b)线缺陷+零折射超构材料滤波器
Fig. 1. Schematic diagram of the filter: (a) Structure of the filter with line defect; (b) structure of the filter with line defect and zero index metamaterial.
图 2 (a)零折射超构材料的光子能带结构; (b), (c)含零折射超构材料滤波器的传输特性
Fig. 2. (a)The band structure of a metamaterial with zero refractive index; (b), (c) transmission characteristics of filter with zero index metamaterials.
图 3 (a)传输谱和(b)缺陷间隙L1随零折射超构材料厚度的变化
Fig. 3. The variations of (a) the transmission spectrum and (b) the width of the defect with the thickness of the zero index metamaterials.
图 4 (a), (b)类狄拉克点频率处滤波器中的波场分布; (c)类狄拉克点附近ZIM的等效参数; (d), (e)滤波器非零折射率透射峰O2, O3的波场分布
Fig. 4. (a), (b) The field distribution in the filter near the Dirac-like point; (c) the effective permittivity and permeability of the ZIM as a function of frequency near the Dirac-like point; (d), (e) the field distribution in the filter at transmission peak O2 and O3 with nonzero refractive index.
图 5 (a)不含ZIM滤波器的传输谱随超构材料厚度的变化; (b)含ZIM滤波器的传输谱随ZIM厚度的变化
Fig. 5. The variations of the transmission spectrum (a) with the thickness of PMs1 for the filter without ZIM and (b) with the thickness of ZIM for the filter with ZIM.
图 6 (a)有限厚度的线缺陷+零折射超构材料滤波器示意图; (b)考虑PMs1中介质柱损耗的滤波器传输谱; (c)考虑ZIM中材料损耗的滤波器传输谱
Fig. 6. (a) Schematic diagram of the finite thickness filter with line defect and zero index metamaterial; (b), (c) transmission spectrum considering different material losses of dielectric columns in defects and in ZIM.
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[1] 陈鹤鸣, 孟晴 2011 物理学报 60 014202
Google Scholar
Chen H M, Meng Q 2011 Acta Phys. Sin. 60 014202
Google Scholar
[2] Mao J D, Li J, Zhou C Y, Zhao H, Sheng H J 2013 Laser Phys. 23 026003
Google Scholar
[3] Meng X J, Li J S, Guo Y, Du H J, Liu Y D, Li S G, Guo H T, Bi W H 2021 J. Opt. Soc. Am. B. 38 1525
Google Scholar
[4] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
Google Scholar
[5] Wang F, Cheng Y Z, Wang X, Qi D, Luo H, Gong R Z 2018 Opt. Mater. 75 373
Google Scholar
[6] John S 1987 Phys. Rev. Lett. 58 2486
Google Scholar
[7] Fan S H, Villeneuve P R, Joannopoulos J D, Haus H A 1998 Opt. Express 3 4
Google Scholar
[8] 罗宇轩, 程用志, 陈浮, 罗辉, 李享成 2023 物理学报 72 044101
Google Scholar
Luo Y X, Cheng Y Z, Chen F, Luo H, Li X C 2023 Acta Phys. Sin. 72 044101
Google Scholar
[9] Chen L, Liao D G, Guo X G, Zhao J Y, Zhu Y M, Zhuang S L 2019 Front. Inform. Technol. Elect. Eng. 20 591
Google Scholar
[10] 杨春云, 徐旭明, 叶涛, 缪路平 2011 物理学报 60 017807
Google Scholar
Yang C Y, Xu X M, Ye T, Miu L P 2011 Acta Phys. Sin. 60 017807
Google Scholar
[11] 陈颖, 王文跃, 于娜 2014 物理学报 63 034205
Google Scholar
Chen Y, Wang W Y, Yu N 2014 Acta Phys. Sin. 63 034205
Google Scholar
[12] 余建立, 沈宏君, 叶松, 洪求三 2012 光学学报 32 1106003
Google Scholar
Yu J L, Shen H J, Ye S, Hong Q S 2012 Acta Opt. Sin. 32 1106003
Google Scholar
[13] Dai Z X, Wang J L, Heng Y 2011 Opt. Express 19 3667
Google Scholar
[14] Chen C, Li X C, Li H H, Xu K, Wu J, Lin J T 2007 Opt. Express 15 11278
Google Scholar
[15] 庄煜阳, 周雯, 季珂, 陈鹤鸣 2015 物理学报 64 224202
Google Scholar
Zhuang Y Y, Zhou W, Ji K, Chen H M 2015 Acta Phys. Sin. 64 224202
Google Scholar
[16] Edwards B, Alù A, Young M, Silveirinha M, Engheta N 2008 Phys. Rev. Lett. 100 033903
Google Scholar
[17] Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C T 2011 Nat. Mater. 10 582
Google Scholar
[18] Cheng Q, Jiang W X, Cui T J 2012 Phys. Rev. Lett. 108 213903
Google Scholar
[19] Vulis D I, Reshef O, Camayd-Munoz P, Mazur E 2019 Rep. Prog. Phys. 82 012001
Google Scholar
[20] Li Y, Chan C T, Mazur E 2021 Light-Sci. Appl. 10 203
Google Scholar
[21] Luo J, Lai Y 2022 Front. Phys. 10 845624
Google Scholar
[22] Silveirinha M G, Engheta N 2006 Phys. Rev. Lett. 97 157403
Google Scholar
[23] Silveirinha M G, Engheta N 2007 Phys. Rev. B 76 245109
Google Scholar
[24] Enoch S, Tayeb G, Sabouroux P, Guerin N, Vincent P 2002 Phys. Rev. Lett. 89 213902
Google Scholar
[25] Ma Y G, Wang P, Chen X, Ong C K 2009 Appl. Phys. Lett. 94 044107
Google Scholar
[26] Edwards B, Alù, Silveirinha M G, Engheta N 2009 J. Appl. Phys. 105 044905
Google Scholar
[27] Luo J, Xu P, Chen H Y, Hou B, Gao L, Lai Y 2012 Appl. Phys. Lett. 100 221903
Google Scholar
[28] Alù A, Silveirinha M G, Salandrino A, Engheta N 2007 Phys. Rev. B 75 155410
Google Scholar
[29] Nguyen V C, Chen L, Halterman K 2010 Phys. Rev. Lett. 105 233908
Google Scholar
[30] Xu J M, Chen L, Zang X F, Cai B, Peng Y, Zhu Y M 2013 Appl. Phys. Lett. 103 161116
Google Scholar
[31] Chan C T, Huang X, Liu F, Hang Z H 2012 PIER B 44 163
Google Scholar
[32] Huang X Q, Chan C T 2015 Acta Phys. Sin. 64 0184208 (in Chinese) [黄学勤, 陈子亭 2015 物理学报64 184208
Google Scholar
Huang X Q, Chan C T 2015 Acta Phys. Sin.64 0184208 (in Chinese)Google Scholar
[33] Wang L G, Wang Z G, Zhang J X, Zhu S Y 2009 Opt. Lett. 34 1510
Google Scholar
[34] Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111
Google Scholar
[35] Jin J F, Liu S Y, Lin Z F, Chui S T 2011 Phys. Rev. B 84 115101
Google Scholar
[36] Moitra P, Yang Y, Anderson Z, Kravchenko I I, Briggs D P, Valentine J 2013 Nat. Photon. 7 791
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